If by "stay" you mean spread microplatisc, that carries no information, then maybe. The jury is still out, but it looks like it'll last a long time.

But plastic is not a good candidate to hold messages for a long time. It degrades in a few years into some unusable stuff. Glass is a much better candidate.

Unless a microbe finds a way to use it as fuel

There's a microbe for everything: https://cen.acs.org/environment/sustainability/Plastics-recy...